Section 5.1 (part 5) - Proving reflexive, symmetric, and transitive

I go through proofs and counterexamples for reflexive, symmetric, and transitive.

[cyrrender]

Hello, thank you for this video! You are the only person I’ve come across that shows the relations in a set written that way (as in without ordered pairs.) Do you know what this is called exactly? I am trying to understand how I can figure out whether a relation like this R = {a, b ∈ ℤ ∧ |a-b| ≤ 3} is reflexive, symmetric, and/or transitive. I can already tell it’s reflexive (I think) but I’m not sure how to show whether or not it’s symmetric and/or transitive. Help or guidance would be much appreciated. Cheers!